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Managerial Accounting
Tenth Canadian Edition
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What You Really Need To Know
Chapter 3: Cost Behaviour: Analysis and Use
A. A variable cost is a cost that varies, in total, in proportion to changes in the level of
activity. Variable costs are constant on a per unit basis.
1. Activity is often measured in terms of the volume of goods produced or
services provided by the organization. However, other measures of activity
may be used for specific purposes such as patients admitted to a hospital,
number of machinery setups performed, number of sales calls made, and so
on.
2. A variable cost is shown graphically in Exhibit 3-1. Note that a variable cost
is a straight line that goes through zero (i.e., the origin) on the graph.
3. A step-variable cost (such as the cost of maintenance worker) is one that can
be obtained only in large blocks and that increases and decreases only in
response to wide changes in the activity level. Variable and step variable costs
are compared in Exhibit 3-3.
B. A fixed cost is a cost that remains constant in total within the relevant range. Fixed
cost per unit varies inversely with changes in activity. As activity increases (decreases),
per unit fixed costs fall (rise). Exhibit 3-5 illustrates this point.
1. Fixed costs can generally be classified into committed and discretionary fixed
costs.
a. Committed fixed costs relate to investments in facilities, equipment, and
the basic organization of a firm. These costs are difficult to adjust in the
short-run.
b. Discretionary fixed costs, often called managed fixed costs, result from
annual decisions by management to spend in certain areas, such as
advertising, research, and management development programs. These
costs are easier to modify in the short-run than committed fixed costs.
2. If there is a big enough change in activity, even committed fixed costs may
change. Exhibit 3-6 illustrates this idea. However, within the band of activity
known as the relevant range, total fixed cost is constant.
C. The relevant range and curvilinear costs.
1. For simplicity, a strict linear relation between cost and volume is usually
assumed. However, many cost relationships are curvilinear, such as illustrated
in Exhibit 3-4.
2. The manager’s straight-line assumption is reasonable since any small portion
of a curvilinear cost can be approximated by a straight line. The relevant
range is the range of activity within which a particular straight line is a valid
approximation to the curvilinear cost.
D. A mixed cost (or semivariable cost) is a cost that contains both variable and fixed cost
elements. Exhibit 3-7 illustrates a mixed cost.
1. Examples of mixed costs include electricity, costs of processing bills, costs of
admitting patients to a hospital, and maintenance.
2. The fixed portion of a mixed cost represents the cost of providing capacity.
The variable portion represents the additional cost of using the capacity.
3. Two common methods exist for estimating the fixed and variable portions of a
mixed cost.
a. Account analysis requires classification of each account under
consideration as variable or fixed. The classification is based on the
analyst’s prior expertise on how costs behave.
b. The engineering approach is a detailed analysis of cost behaviour
based on an industrial engineer’s evaluation of the inputs required to
carry out a particular activity and the price of those inputs.
E. Cost formula for a mixed cost.
1. The fixed and variable cost elements of a mixed cost can be expressed as a
cost formula, which can be used to predict costs at all levels of activity within
the relevant range. This formula is expressed as follows:
Y= a + bX
where:
Y = dependent variable (the total mixed cost)
a = vertical intercept (the total fixed cost)
b = slope of the line (the variable cost)
X = independent variable (the activity level)
2. Each of the methods discussed below can be used to estimate the variable cost
per unit, b, and the total fixed cost, a, based on data from prior periods. Then
with the use of the cost formula, the expected amount of total cost, Y, can be
computed for any expected activity level, X, within the relevant range.
F. The analysis of a mixed cost begins with records of past cost and activity. The first
step is to plot the cost and activity data on a scattergraph. The cost is represented on the
vertical, Y, axis and activity is represented on the horizontal, X, axis.
1. If the scattergraph plot indicates that the relation between cost and activity is
approximately linear (i.e., a straight line), the analysis can proceed to the next
stage of estimating the variable cost per unit of activity and the fixed cost per
period.
2. A quick and dirty way to estimate the variable and fixed costs is to draw a
straight line on the scattergraph plot. The intercept of the line with the vertical
axis is the estimated total fixed cost. The slope of the line is the estimated
variable cost per unit of activity.
G. The high-low method analyzes the variable and fixed elements of a mixed cost based
on using the highest and lowest levels of activity.
1. The high-low method uses the "rise over run" formula for the slope of a
straight line. The difference in cost observed between the two extremes (i.e.,
the rise) is divided by the change in activity (i.e., the run) to estimate the
amount of variable cost. The formula is:
Variable cost
per unit of activity
=
Change in cost
Change in activity
2. The estimated variable cost per unit of activity (i.e., variable rate) is then used
to estimate the fixed cost as follows:
Total cost at the high (low) activity level
Less variable portion:
Variable rate × high (low) activity level
Fixed portion of the mixed cost
$XXX
XXX
$ XXX
3. The high-low method is easy to use but not reliable. It is based on costs and
activity for only two periods—the periods with the highest and lowest levels
of activity. Other data are ignored and these two periods may not be
representative of typical cost behaviour.
H. The least-squares regression method of analyzing a mixed cost fits a straight line,
called a regression line, to cost and activity data using a formula explained in the
appendix to the chapter.
1. The least-squares regression formula calculates the slope and intercept of the
straight line that minimizes the sum of the squared errors from the regression
line. Because the computations are fairly complex, it is a good idea to use
statistical software or a spreadsheet to do the calculations.
2. Least-squares software provides a number of useful statistics including R2.
The R2 indicates the percentage of variation in the dependent variable (cost)
explained by variation in the independent variable (activity). The value of R2
ranges from 0 to 100% with higher percentages indicating a better fit.
3. Multiple regression analysis should be used when more than one factor causes
a cost to vary. This technique is beyond the scope of the book.
I. The contribution approach to preparation of an income statement emphasizes cost
behaviour.
1. The traditional format for income statements groups expenses into functional
categories:
Sales ..................................................
Less: Cost of Goods Sold .................
Gross Margin ...................................
Less: Admin. and Selling Expense ..
Operating Income ............................
$XXX
XXX
XXX
XXX
$XXX
2. The contribution approach, in contrast, groups expenses according to their cost
behaviour.
Sales .....................................................
Less: Variable Expenses .....................
Contribution Margin ...........................
Less: Fixed Expenses ..........................
Operating Income ...............................
$XXX
XXX
XXX
XXX
$XXX
3. Note that the contribution margin is determined by deducting variable
expenses from sales.
4. The contribution approach is very useful to managers for internal reports since
it emphasizes the behaviour of costs. As you will see in later chapters, this is
very important in planning, budgeting, controlling operations, and in
performance evaluation. However, in external reports the traditional format
that emphasizes cost by function is often used.
Appendix 3A: Least-Squares Regression Calculations
A. The formulas for computing the variable cost per unit, b, and total fixed cost, a, using
the least-squares regression method are:
b
n   XY     X   Y 
n   X2     X 
2
a
 Y  b  X
n
where
X = the level of activity (independent variable)
Y = the total mixed cost (dependent variable)
a = the total fixed cost (the vertical intercept of the line)
b = the variable cost per unit of activity (the slope of the line)
n = the number of observations
∑ = the sum across all n observations.
B. The appendix illustrates how to use built-in functions in Microsoft Excel to do a
regression analysis.
What To Watch Out For (Hints, Tips and Traps)

The chapter introduces a new cost concept – mixed costs – and shows how mixed
costs can be broken down into their basic fixed and variable elements. Be sure to
carefully study the section titled "The Analysis of Mixed Costs" found midway
through the chapter. Pay particular attention to the methods of deriving a cost
formula and how it is used to predict future costs at various levels. Make sure you
understand and can interpret the elements of the equation Y = a + bX. You need
to understand this equation to complete many of the homework exercises and
problems. At the end of the chapter, a new format for the income statement is
introduced that emphasizes cost behaviour. Exhibit 3-11 illustrates the format of
the contribution income statement. This format should be studied very carefully –
you will use it frequently throughout the rest of the book

Variable, fixed and mixed costs are defined relative to the level of activity (or
volume). A variable cost remains constant on a per unit basis, but changes in total
in direct relation to changes in volume. A fixed cost remains constant in total
amount, but changes, if expressed on a per unit basis, inversely with changes in
volume. A fixed cost may appear variable, since it may fluctuate from period to
period in total, however, these if these fluctuations are not in direct relation to the
change in level of activity then it is not variable by definition, it must be either a
fixed cost or a mixed cost. For instance, even straight-line depreciation can
fluctuate from period to period (due to additions, disposals, and changes in
estimated useful life or residual value), however, the depreciation would still be
considered a fixed cost as the fluctuations are not directly related to the change in
level of activity.

Although the high-low method of analyzing mixed costs is often used by
managers because of its simplicity, it essentially utilizes only two data points and
draws a straight-line between the highest activity level data point and the lowest
activity level data point. All other data points are ignored and this may seriously
misrepresent the true cost relationship. Furthermore, sometimes the high and low
activity levels don’t coincide with the high and low amounts of cost.
Nevertheless, the highest and the lowest levels of activity are always used to
analyze a mixed cost under the high-low method.